Appendix II
847'
(b)
-,and 2nd moment = 2 {PPI x e x (PN)2}
(<? x // x PQX x PN) ... ... by substitution from (a)
(<? x #* x PQ2) ...... by substitution from (£)
= ffi x 2 0 x PQ2) = A2/fr2
r moments may be similarly proved.
the construction to beam sections, we must first find
Imagine any given section ab (Fig. Bio). Find its
-----^1 LINE OF \CU LIMITING STRESS j.
X,
o-f
^b X
loment Ax, round xx say, using any height //. Dealing only
he right-hand half for simplicity, we have from the definition
itre-of-gravity,
A^ = A G Hence, G = ——
gives the height of neutral axis z z by a much more simple
ccurate method than those on p. 432, especially if a plani-
is obtainable. We next require I, the 2nd moment, round
ting preferably the reference distance y to line of limiting
in constructing the curves. Treating the left side, to avoid
ion, every horizontal strip is referred to //, and its projection
to ^producing if necessary, till the original strip is crossed ;
hus the areas a± a\ are found, on opposite sides of the
L] centre line. Continuing the process on areas a± a\, the